Frictionless Technology Diffusion: The Case of Tractors
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Frictionless Technology Diffusion: The Case of Tractors
∗
Rodolfo E. Manuelli Ananth Seshadri
March, 2003
Abstract
Empirical evidence suggests that there is a long lag between the time a new technology
is introduced and the time at which it is widely adopted. The conventional wisdom is that
these observations are inconsistent with the predictions of the frictionless neoclassical model.
In this paper we show this to be incorrect. Once the appropriate driving forces are taken
into account, the neoclassical model can account for ‘slow’ adoption. We illustrate this by
developing an industry model to study the equilibrium rate of diffusion of tractors in the U.S.
between 1910 and 1960.
1 Introduction
Understanding the determinants of the rate at which new technologies are created and adopted
is a critical element in the analysis of growth. Even though modeling equilibrium technology
creation can be somewhat challenging for standard economic theory, understanding technology
adoption should not be. SpeciÞcally, once the technology is available, the adoption decision is
equivalent to picking a point on the appropriate isoquant. Dynamic considerations make this
∗
University of Wisconsin-Madison & NBER and University of Wisconsin-Madison, respectively. We would like to
thank NSF for Þnancial support through our respective grants. We are indebted to William White who generously
provided us with a database containing tractor production, technical characteristics and sale prices, and to Paul
Rhode who shared with us his data on prices of average tractors and draft horses. We thank Hal Cole, Jeremy
Greenwood and seminar participants at UCLA, USC - Marshall School of Business and University of Rochester for
their very helpful comments. Naveen Singhal provided excellent research assistance.
1calculation more complicated, but they still leave it in the realm of the neoclassical model. A
simple minded application of the theory of the Þrm suggests that proÞtable innovations should be
adopted instantaneously, or with some delay depending on various forms of cost of adjustment.
The evidence on adoption of new technologies seems to contradict this prediction. One of the
‘stylized facts’ in this literature is that the adoption rate is S-shaped and that it takes a long time
until a large fraction of units adopts the new technology. Several studies – e.g. Griliches (1957),
Gort and Klepper (1982) and Jovanovic and Lach (1997), among others – have documented the
logistic shape of the diffusion curve. Jovanovic and Lach (1997) report that, for a group of 21
innovations, it takes 15 years for its diffusion to go from 10% to 90%, the 10-90 lag. They also
cite the results of a study by Grübler (1991) covering 265 innovations who Þnds that, for most
diffusion processes, the 10-90 lag is between 15 and 30 years.1
In response to this apparent failure of the simple neoclassical model, a large number of papers
have introduced ‘frictions’ to account for the ‘slow’ adoption rate. These frictions include, among
others, learning-by-doing (e.g. Jovanovic and Lach (1989), Jovanovic and Nyarko (1996), Green-
wood and Yorukoglu (1997), Felli and Ortalo-Magné (1997), and Atkeson and Kehoe (2001)),
vintage human capital (e.g. Chari and Hopenhayn (1994) and Greenwood and Yorukoglu (1997)),
informational barriers and spillovers across Þrms (e.g. Jovanovic and Macdonald (1994)), resis-
tance on the part of sectoral interests (e.g. Parente and Prescott (1994)), coordination problems
(e.g. Shleifer (1986)) and search-type frictions (e.g. Manuelli (2002)).
In this paper we take, in some sense, one step back and revisit the implications of the neoclas-
sical frictionless model for the equilibrium rate of diffusion of a new technology. The application
that we consider throughout is another famous case of ‘slow’ adoption: the farm tractor in Amer-
ican agriculture.2 Following Lucas (1978), we study an industry model in which managers (farm
1
There are studies of speciÞc technologies that also support the idea of long lags. Greenwood (1997) reports that
the 10-90 lag is 54 years for steam locomotives and 25 years for diesels, Rose and Joskow’s (1990) evidence suggest
a 10-90 lag of over 25 years for coal-Þred steam-electric high preasure (2400 psi) generating units, while Oster’s
(1982) data show that the 10-90 lag exceeds 20 years for basic oxygen furnaces in steel production. However, not
all studies Þnd long lags; using Griliches (1957) estimates, the 10-90 lag ranges from 4 to 12 years for hybrid corn.
2
Using the fraction of farms that operate a tractor as our measure of diffusion, the 10-90 lag is at least 35 years
in the case of tractors.
2operators) differ in terms of their skills. We assume that the technology displays constant returns
to scale in all factors, including managerial talent. In order to ignore frictions associated with in-
divisible inputs, we study the case in which there are perfect rental markets for all inputs.3 Each
farm operator maximizes proÞts choosing the mix of inputs. Given our market structure, this
is a static problem. In addition, each manager has to make a discrete location choice: stay and
continue farming, or migrate to an urban area and earn urban wages. We assume that migration
is costly and, in fact, the cost of migration is the only non-convexity in our setting. The migration
decision is dynamic. We take prices and the quality of all inputs as exogenous and we let the
model determine the price of one input, land, so as to guarantee that demand equals the available
stock.
Our model has three features that inßuence the diffusion rate: exogenous changes in the price
of inputs other than the new technology, exogenous changes in the quality of the technology, and
endogenous selection of Þrms (farm managers) out of the industry. We show that when these three
factors are taken into account, the model is very successful at predicting the pattern of diffusion
of tractors.
Our work emphasizes that farmers had a choice between a ‘new’ technology (tractors) and an
‘old’ technology (horses). However, a simple computation based on prices of tractors and horses
cannot explain the observed pattern of diffusion. We study the impact on adoption of the dramatic
decrease in horse prices and Þnd that it only had a marginal impact on tractor adoption. In the
model labor is an input that must be combined with tractors and horses to produce ‘traction
services’. We Þnd that changes in wage rates play a critical role in explaining why the adoption
of the tractor was delayed until the 1940s: Only at this time did real wages increase substantially,
and this made the horse-technology less attractive.
In addition to the direct effect, the change in real wages has an indirect effect: it affects
migration decisions. In equilibrium, wage increases induce marginal farm operators to leave the
agricultural sector. Equilibrium migration is such that the distribution of skills of the remaining
farmers improves over time, and this change also results in higher levels of adoption of tractors.
3
This, effectively, eliminates the indivisibility at the individual level. Given the scale of the industry that we
study, indivisibilities at the aggregate level are not relevant.
3Finally, we estimate the change in the ‘quality’ of a tractor using standard hedonic techniques.
We Þnd that, even though the amount of ‘tractor services’ per tractor grew rapidly in the 1920s,
the increase was not large enough to induce widespread adoption. Our estimates of tractor quality
show a substantial increase in the post World War II period, and this coincides with the era of
rapid adoption.
We choose the parameters of the model so that it reproduces several features of the U.S.
agricultural sector in 1910. We then use the calibrated model, driven by exogenous changes in
prices, to predict the number the tractors (and other variables) for the entire 1910-1960 period.
The model is very successful at accounting for the diffusion of the tractor and the demise of the
horse. The correlation coefficient between the model’s predictions and the data is 0.99 for tractors
and 0.98 for horses. We conclude that there is no tension between a frictionless neoclassical model
and the rate at which tractors diffused in U.S. agriculture: the reason why diffusion was ‘slow’ is
because it was not cost effective to use tractors more intensively.
In order to ascertain what are the essential features of the model that account for such a good
Þt, we study several counterfactuals. We analyze versions of the model that keep wages, horse
prices and tractor quality Þxed at their 1910 levels, and another version that ignores selection
of Þrms (farmers) out of the industry. These alternative speciÞcations fail to match the data in
several important dimensions.
The paper is organized as follows. In section 2 we present a brief historical account of the
diffusion of the tractor and of the price and quality variables that are the driving forces in our
model. Section 3 describes the model, and Section 4 discusses calibration. Sections 5 and 6 present
our results, and section 7 offers some concluding comments.
2 Some History
This section presents some evidence the use of tractors and horses by U.S. farmers, on the behavior
of wages and employment in the U.S. agricultural sector, and on the changes in the size distribution
of farms.
Diffusion of the Tractor. The diffusion of the tractor was not unlike most other technologies, it
4had a characteristic S-shape. Figure 1 plots the number of tractors on American farms. Diffusion
was slow initially. The pace of adoption speeds up after 1940.
5000
25000
Horses and Mules
4000
Tractors
Horses and Mules (in '000)
20000
Tractors (in '000)
3000
15000
2000
10000
1000
5000
0
0
1910 1920 1930 1940 1950 1960
Year
Figure 1: Horses, Mules and Tractors in Farms, 1910-1960
As the tractor made its way into the farms, the stock of horses began to decline. In 1920, there
were more than 26 million horses and mules on farms. Thereafter, this stock began to decline
and by 1960, there were just about 3 million. While the tractor was primarily responsible for this
decline, it should be kept in mind that the automobile was also instrumental in the elimination of
the horse technology. As in the case of other technologies, investment in horses –the ‘dominated’
technology– was positive, even as the stock declined.
Real Prices for Tractors and Horses. Figure 2 plots the real price of a mid-size tractor and
5a pair of draft horses between 1910 and 1960.4 Between 1910 and 1920, there is a sharp decline
in the price of tractors which is partially reversed in the 1930s. In the 1940s and 1950s prices
are lower and comparable to those prevailing in 1920s. One simple conclusion from this evidence
is that farmers should have adopted tractors in 1920 at the same rate they did in the 1940s and
1950s. They did not. This observation lies behind the idea that adoption was slow. White (2000)
collected data on some tractor characteristics and estimated a quality adjusted price for a tractor.
The resulting series –labeled Tractor-quality adjusted in Figure 2– shows a steep decline until
the mid-1920s, but very small changes after this. Thus, changes in the price of the technology –in
the absence of frictions– appear to be insufficient to explain the pattern of adoption documented
in Figure 1.
Farm Real Wage Rates and Employment. Real wages in the agricultural sector remained
stagnant from 1910 till about 1930, fell by half between 1930 and 1934, and then doubled between
1940 and 1950. If the tractor was labor-saving, rising wages after 1940 would likely speed up
adoption since holding on to the more labor intensive horse technology will be unproÞtable. The
falling wages in the early thirties might also go towards explaining the reluctance of farmers to
switch to tractors during the same time period.
Man-hours on farms remained fairly constant between 1910 and 1930, and then fell by 76%
between 1930 and 1970. Farm population decreased dramatically too. In 1910, there were 11.67
million farm workers (full-time equivalents). By 1960, this number had fallen to 5.97 million.
Distribution of Land-Holding Patterns. The distribution of land-holding patterns underwent
a signiÞcant change between the years 1910 and 1960. The average size of a farm more than
doubled, and land in large-sized farms (size above 1000 acres) tripled between 1920 and 1960.
Land in mid-size farms (500-999 acres in size) also increased, though the increase was far less
spectacular than its larger counterparts. As expected, land in smaller farms of size less than 500
acres decreased, with most of the decline after 1940.
Alternative Explanations. The standard approach to studying the diffusion of the tractor is
based on the ‘threshold’ model originally introduced by David (1966). In its simplest form, the
4
The data are from Olmstead and Rhode (2001). We thank Paul Rhode for providing the data.
6120
100
80
Real Price
60 Tractor
40
Horse
20
Tractor - quality adjusted
0
1910 1920 1930 1940 1950 1960
Year
Figure 2: Real Prices for Tractors and Horses. 1910-1960
model takes as given the size of the farm (in acres) and considers the costs of different combinations
of horse-drawn and tractor-drawn technologies required to produce a given amount of services.
By choosing the cost minimizing technology, the model selects the type (size) of farm that should
adopt a tractor. The predictions of the model – given the size distribution of farms – are then
compared with the data. These calculations Þnd that in the 1920’s and early 1930’s, U.S. farmers
were too slow to adopt the relatively new tractor technology. Allowing for imperfect capital
markets (Clarke (1991)) or introducing uncertainty about the value of output (Lew (2001)) help
improve the Þt of the model, but not to the point where it is consistent with the evidence.
More recently Olmstead and Rhode (2001) estimate that changes in the price of horses and
in the size distribution delayed, to some extent, the adoption of tractors. In their model the size
7distribution is exogenous. White (2000) emphasizes the role of prices and quality of tractors. Using
a hedonic regression, he computes a quality-adjusted price series for tractors. White conjectures
that the increase in tractor quality should be taken into account to understand adoption decisions.
3 A Simple Model of Farming and Migration
Our approach is to model technology adoption using a standard proÞt maximization argument,
supplemented by a simple model of migration-choice along the lines of Becker (1964) and Sjaastad
(1962). We consider a setting in which farm operators are heterogeneous. Each individual has
a level of ‘farm organizational ability’ or ‘skill’ denoted by e. The distribution of skills in the
population of potential farmers is given, and denoted by µ. However, the distribution of skills
among actual farmers is endogenously determined by the model. In each period, a farmer can
either stay (and farm) or migrate to an urban area. To simplify the analysis, we assume that
the migration decision is irreversible: once a farmer leaves the rural sector, he cannot return to
farming.5
If the farmer decides to stay, and operate the farm, he needs to decide how many tractors,
horses, acres of land and labor to rent in spot markets. We consider the case in which there are
perfect markets for all inputs. Thus, as is standard in the theory of the Þrm, indivisibilities at the
individual farm level are irrelevant.6 This implies that our model can be used to predict the total
number of tractors but not their distribution across farms.
Each farmer maximizes the present discounted value of utility taking prices as given. If the
individual is in the farm sector, he chooses, in every period, the quantity of tractor, horse, land
and labor services in order to produce agricultural output. The one period proÞt of a farmer with
5
Given the relevant values of the cost of migration and the potential gains of reverse migration, we will argue
later that this is not as extreme an assumption as it sounds.
6
Olmstead and Rhode (2001) provide evidence of the prevalence of contract work, i.e. of instances in which a
farmer provides ‘tractor services’ to other farms.
8managerial skill level e is given by,
πt (qt , ct , wtF , e) ≡ max pct F (kt , ht , nt , at , e) −
kt ,ht ,nt ,at
t
X
[qkt (τ ) + ckt (τ )]mkt (τ ) − [qht + cht ]ht − wtF n̄t − [qat + cat ]at ,
τ =−∞
where F (kt , ht , nt , at , e) is a standard production function which we assume to be homogeneous
of degree one in all inputs, including managerial skill, e,7 kt is the demand for tractor services,
ht is the demand for horse services (which we assume proportional to the stock of horses), nt =
(nht , nkt , nyt ) is a vector of labor services corresponding to three potential uses: operating horses,
nht , operating tractors, nkt , or other farms tasks, nyt , and at is the demand for land services
(which we assume proportional to acreage), and n̄t = nht + nkt + nyt is the total demand for labor.
On the cost side, qht + cht is the full cost of operating a draft of horses. The term qht is the
rental price of a horse, and cht includes operating costs (e.g. feed and veterinary services). The
term qat + cat is the full cost of using one acre of land, and wtF is the cost of one unit of (farm)
labor. Effective one period rental prices for horses and land (two durable goods) are given by
(1 − δ jt )pjt+1
qjt ≡ pjt − , j = h, a,
1 + rt+1
where δ jt are the relevant depreciation factors, and rt is the interest rate.
Since we view changes in the quality of tractors as a major factor driving the decision to adopt
the technology, we speciÞed the model so that we could capture such variations. SpeciÞcally, we
assume that tractor services can be provided by tractors of different vintages according to
t
X
kt = mkt (τ )k̃t (τ ),
τ =−∞
where k̃t (τ ) is the amount of tractor services provided by a tractor of vintage τ (i.e. built in period
τ ) at time t, and mkt (τ ) is the number of tractors of vintage τ operated at time t. We assume
that the amount of tractor services provided at time t by a tractor of vintage τ is given by,
k̃t (τ ) ≡ v(xτ )(1 − δ kτ )t−τ ,
7
The assumption that F depends on managerial skill, e, follows the work of Lucas (1978). As in Lucas’ framework,
its main role is to endogenously generate changes in the size distribution of farms.
9where δ kτ is the depreciation rate of a vintage τ tractor, and v(xτ ) maps model-speciÞc charac-
teristics, the vector xτ , into an overall index of tractor ‘services’ or ‘quality.’ Thus, our model
assumes that the characteristics of a tractor are Þxed over its lifetime (i.e. no upgrades), and that
tractors depreciate at a rate that is (possibly) vintage speciÞc. The rental price of a tractor is
given by
pkt+1 (τ )
qkt (τ ) = pkt (τ ) − ,
1 + rt+1
where pkt (τ ) is the price at time t of a t − τ year old tractor, while the term ckt (τ ) captures the
variable cost (fuel, repairs) associated with operating one tractor of vintage τ at time t.
The function πt (qt , ct , wtF , e) captures the payoff in period t to being a farmer. Instead of
farming, an individual with skill level e can make an (irreversible) migration decision. If he
chooses to migrate to an urban area at time t, he receives a payoff given by
∞
X
VtU ≡ U
Rt (j)wt+j − ϕ,
j=0
U is a measure of the utility associated with working in an urban area at time t + j, ϕ
where wt+j
is the Þxed cost of migration, and
1 if j = 0
Rt (j) = ,
Πj (1 + r )−1 if j ≥ 1
s=1 t+s
is the relevant discount factor.
It follows that the utility of an individual with skill e who starts period t in a rural area (i.e.
is a potential farmer) satisÞes the following Bellman equation
© ª
Vt (e) = max VtU , πt (e) + Rt (1)Vt+1 (e) .
Given our assumption that F is increasing in e, it follows that Vt (e) is also increasing in e.
Moreover, if a farmer with skill level e chooses not to migrate, then all farmers with skill level
e0 ≥ e will not migrate either. Put differently, equilibrium migration is fully described, for each
t, by the level of skill of the marginal farmer, e∗t . Our assumption that the migration decision is
irreversible, implies that the equilibrium sequence {e∗t } is non-decreasing.
10Optimal choices of inputs and output by a farmer with skill level e are completely summarized
by the Þrst order conditions of proÞt maximization. The resulting demand for input functions for,
each e, are denoted by 8
mt = m(qt , ct , wtF , e),
where m ∈ {k, h, a, n̄} indicates the input type, qt is a vector of rental prices, and ct is a vector of
operating costs, and wtF denotes real wages in the farm sector.
Given that agricultural prices are largely set in world markets, and that domestic and total
demand do not coincide, we impose as an equilibrium condition that the demand for land equal
the available supply. Thus, land prices are endogenously determined.
3.1 Aggregate Implications
In this section we show how to compute the implications of our simple model for sector-wide
aggregates. To this end we need to sum individual factor demands over all possible skill types.
3.1.1 The Number of Farms and Labor in Farms
R∞
Let the measure of potential farmers be N̄ . We assume that N̄ = 0 µ(de), for some measure µ.
This measure captures the exogenous distribution of skills. let e∗t be the ‘marginal’ farmer at time
Re
t; then, the number of farmers with ability levels less than or equal to e at time t is e∗ µ(ds), for
t
e≥ e∗t , and 0 for e < e∗t .
This distribution is time-varying and endogenously determined. The
R∞
number of active farmers (and the number of farms)9 at t is simply Nf t = e∗ µ(de).
t
Let, êt be the value of e that satisÞes
Vt (êt ) ≡ VtU .
© ª
Then, e∗t evolves according to e∗t = min e∗t−1 , êt . This formulation imposes the equilibrium
condition that the the marginal farmer be indifferent between migrating or staying, or its identity
8
To be precise, the demand functions depend on current and future prices. Even though the pure demand decision
is static due to our assumption of perfect rental markets, the migration decision implies that future prices inßuence
current demand through their impact on the identity of the farmers who remain in the rural sector, i.e. the level of
e.
9
Our model does not distinguish farms from farm operators.
11is unchanged from the previous period. The condition Vt (êt ) = VtU is not a simple comparison.
The reason is that Vt (e) depends on all prices and, in our model, the price of land is determined
endogenously (and a function of the distribution µ and the cutoff point e∗t ). Hence, obtaining êt
requires the computation of a Þxed point at each t.
If each farmer has an endowment of n̂ man/year equivalent (including family workers), the
total number of man/year equivalent labor provided by farmers is n̂Nf t , while the total number
of man/year individuals hired is10
Z ∞ £ ¤
Nst = max n̄(qt , ct , wtF , e) − n̂, 0 µ(de). (1)
e∗t
The ratio of hired to total labor is given by
R∞ £ F
¤
Nst e∗t max n̄(qt , ct , wt , e) − n̂, 0 µ(de)
ηt = = R∞ F
(2)
Nt e∗ n̄(qt , ct , wt , e)µ(de)
t
3.1.2 Tractors, Horses and Land
The aggregate demand for tractor services at time t, Kt is given by
Z ∞
Kt = k(qt , ct , wtF , e)µ(de), (3)
e∗t
while the number of tractors purchased at t, mkt is
Kt − (1 − δ kt−1 )Kt−1
mkt = . (4)
v(xt )
The law of motion for the stock of tractors (in units), Kt , is11
Kt = (1 − δ kt−1 )Kt−1 + mkt . (5)
10
This formulation assumes that if a farmer’s demand for labor, nt (qt , ct , wtF , e) falls short of his endowment, n̂,
he can sell the difference in the agricultural labor market. This assumption is the natural analog of the perfect
rental markets for tractors, horses, and land.
11
An alternative measure of the stock of tractors is given by Kt+1 = Kt + mkt+1 − mkt−T were T is the lifetime
of a tractor of vintage t − T . This alternative formulation assumes that tractors are of the one-hose shay variety
and that after T periods they are scrapped.
12We assume that horse services are proportional to the stock of horses and, by choice of a
constant, we set the proportionality ratio to one. Thus, the aggregate demand for horses is
Z ∞
Ht = h(qt , ct , wtF , e)µ(de). (6)
e∗t
We let the price of land adjust so that the demand for land predicted by the model equals the
total supply of agricultural land denoted by At . Thus, given wages, agricultural prices and horse
and tractor prices, the price of land, pat , adjusts so that
Z ∞
At = a(qt , ct , wtF , e)µ(de). (7)
e∗t
3.2 Modeling Tractor Prices
From the point of view of an individual farmer the relevant price of tractor is qkt (τ ) : the price
of tractor services corresponding to a t − τ year old tractor. Unfortunately, data on these prices
are not available. However, given a model of tractor price formation, it is possible to determine
rental prices for all vintages using standard, no-arbitrage, arguments.
As indicated above, we assume that a new tractor at time t offers tractor services given by
k̃t (t) = v(xt ), where v(xt ) is a function that maps the characteristics of a tractor into tractor
services. We assume that, at time t, the price of a new tractor is given by
v(xt )
pkt = .
γ ct
In this setting γ −1
ct is a measure of markup over the level of quality. If the industry is com-
petitive, it is interpreted as the amount of aggregate consumption required to produce one unit
of tractor services using the best available technology xt .12 However, if there is imperfect com-
petition, it is a mixture of the cost per unit of quality and a standard markup. For the purposes
of understanding tractor adoption we need not distinguish between these two interpretations: any
factor –technological change or variation in markups– that affects the cost of tractors will have
an impact on the demand for them. In what follows we ignore this distinction, and we label γ ct
as productivity in the tractor industry.
12
We assume that the cost of producing ‘older’ vectors xt is such that all Þrms choose to produce using the newest
new technology.
13It is possible to show (see the Appendix) that no arbitrage arguments imply that
· ¸
γ
qkt (t) = pkt 1 − Rt (1)(1 − δ kt ) ct + (1 − ∆t )C(t + 1, T − 1), (8)
γ ct+1
where
v(xt )(1 − δ kt )
∆t = ,
v(xt+1 )
T
X −1
C(t + 1, T − 1) ≡ Rt+1 (j)ckt+1+j ,
j=0
given that T is the lifetime of a tractor, and ckt is the cost of operating a tractor in period t.
This expression has a simple interpretation. The Þrst term, 1 − Rt (1)(1 − δ kt ) γγ ct , translates
ct+1
the price of a tractor into its ßow equivalent. If there were no changes in the unit cost of tractor
quality, i.e. γ ct = γ ct+1 , this term is just that standard capital cost, (rt+1 + δ kt )/(1 + rt+1 ). The
second term is the ßow equivalent of the present discounted value of the costs of operating a tractor
from t to t + T − 1, C(t + 1, T − 1). In this case, the adjustment factor, 1 − ∆t , includes more
than just depreciation: total costs have to be corrected by the change in the ‘quality’ of tractors,
v(xt )
which is captured by the ratio v(xt+1 ) .
To compute qkt (t) we need to separately identify v(xt ) and γ ct .13 To this end we speciÞed that
the price of a tractor of model m, produced by manufacturer k at time t, pmkt , is given by
pmkt = e−dt ΠN m λj 8mt
j=1 (xjt ) e ,
where xm m m m
t = (x1t , x2t , ...xN t ) is a vector of characteristics of a particular model produced at time
t, the dt variables are time dummies, and Emt is a shock. This formulation is consistent with
the Þndings of White (2000).14 We used data on prices, tractor sales and a large number of
characteristics for almost all models of tractors produced between 1919 and 1955 to estimate
this equation. In the Appendix, we describe the data and the estimation procedure. Given our
13
It is clear that all that is needed is that we identify the changes in these quantities.
14
Formally, we are assuming that the shadow price of the vector of characteristics xt does not change over time.
This is not essential, and the results reported by White (2000), Table 10, can be interpreted as allowing for time-
varying shadow prices. Comparing the results in Tables 10 and 11 in White (2000) it does not appear that the extra
ßexibility is necessary.
14estimates of the time dummy, dˆt , and the price of each tractor, p̂mkt , we computed our estimate
of average quality, v̄(xt ) as
v̄(xt ) = p̄kt γ̂ ct ,
where
X
p̄kt = smkt p̂mkt ,
m
dˆt
γ̂ ct = e ,
with smkt being the share of model m produced by manufacturer k in total sales at time t. The
resulting time-series for v̄(xt ), γ̂ ct and p̄kt are shown in Figure 3.
400
300 Gamma
Index, 1920 = 100
200
v(x)
100
Price
0
1920 1930 1940 1950
Year
Figure 3: Tractor Prices, Quality and Productivity. 1920-1955. Estimation Results.
15Even though the real price of a tractor does not show much of trend after 1920, its components
do. Over the whole period our index of quality doubles, and our measure of productivity shows
a substantial, but temporary increase in the 1940s, with a return to trend in the 1950s. In the
1920-1955 period γ ct more than doubles. Thus, during this period there were substantial increases
in quality and decreases in costs; however, these two factors compensated each other, so that the
real price of a tractor shows a modest decrease.
4 Steady States and Calibration
At the steady state all variables are constant. We denote the interest rate by R = (1 + r)−1 .
The steady state version of the demand for factors is m = m(q, c, wF , e) for m ∈ {k, h, a, n̄}. To
compute steady state aggregates, we use the endogenous distribution of skills of farm operators,
which is completely summarized by e∗ and µ.
Let the steady state proÞt ßow be denoted π(q, c, wF , e). Then, the no-migration condition in
the steady state is
rϕ
π(q, c, wF , e∗ ) = wU −
.
1+r
Equilibrium in the land market requires that the appropriate version of (7) hold. Given this,
it follows that average farm size , ā, is given by
R∞ F
∗ a(q, c, w , e)µ(de)
ā = e . (9)
Nf
Assuming that there is no change in tractor quality at the steady state, the number of tractors
follows from the appropriate version of (4) and (5) it is given by
R∞ F
∗ k(q, c, w , e)µ(de)
K= e . (10)
v(x)
The model’s prediction for the demand for hired labor, the ratio of hired to total labor and
horses follow from the steady state versions of (1), (2), and (6). The model’s prediction for total
farm output, Y, is Z ∞
Y= y(q, c, wF , e))µ(de),
e∗
where y(q, c, wF , e) is the value of output of a farm with managerial skill e at the prices corre-
sponding to the steady state.
164.1 Model SpeciÞcation and Calibration
We consider the following speciÞcation of the farm production technology
F c (yI , e) = Act yIαc e1−αc ,
α
yI = F y (z, ny , a) = z αzy ny ny a1−αzy −αny ,
z = F z (zk , zh ) = [αz (zk )−ρ + (1 − αz )zh−ρ ]−1/ρ ,
zk = F k (k, nk ) = [αk k −ρ + (1 − αk )n−ρ
k ]
−1/ρ
,
zh = F h (h, nh ) = Ah hαh n1−α
h
h
.
This formulation captures the idea that farm output depends on services produced by tractors,
zk , services produced by horses, zh , labor, nj , j = y, h, k, and managerial skills, e. We take a
standard approach and use a Cobb-Douglas formulation except in two cases. We assume that
the elasticity of substitution between tractors and labor in the production of tractor services is
1/(1 + ρ). Since we assume that the elasticity of substitution between horses and labor is one, this
formulation allows us to capture potential differential effects of a change in the wage rate upon
the choice between tractor and horses. Second, we also assume that basic tractor services, zk , and
horse services, zh , are combined with elasticity of substitution 1/(1 + ρ) to produce power services,
z.
We specify that exogenous technological evolves according to Act = eγt . The technology is
completely speciÞed by 9 parameters: (γ, Ah , αc , αzy , αny , αz , αk , αh , ρ).
We assume that the distribution µ is log-normal with mean µ̂ and standard deviation σ. In
addition to these two parameters, it is necessary to select values for the discount factor β, the cost
of migration, ϕ, the man/year equivalent of a farm family, n̂. This is a total of 14 parameters.
We assume that β = 0.96, and that n̂ = 2. This last value is equivalent to specifying that the
average farm family contributes labor equivalent to 2 workers. Since we could not Þnd reliable
estimates of ϕ we considered initially a value of ϕ equal to one year of average earnings.15 We
performed some sensitivity analysis and varied ϕ between a half and one and a half of average
15
Kennan and Walker (2003) estimate that for high school graduates the cost of moving between urban areas is
about $250,000. Thus, our assumption of one year in the baseline case is conservative.
17yearly earnings, and our Þndings remain essentially unchanged.
We take the process {Act } to correspond to total factor productivity. Even though there are
estimates of the evolution of TFP for the agricultural sector, it is by no means obvious how to use
them. The problem is that, conditional on the model, part of measured TFP changes is due to
changes in the quality of tractors, v(xt ), as well as the rate of diffusion of tractors. Thus, in our
model, conventionally measured TFP is endogenous. To compute (truly) exogenous TFP we used
the following identiÞcation assumption: TFP is adjusted so that the model’s prediction for the
change in output between 1910 and 1960 match the data. This gives us an estimate of γ, which,
in this case, is approximately 1.5% per year.
The remaining parameters of the model were picked to minimize the differences between model
and data for the year 1910. We used two sets of moments from the 1910 agricultural sector to
calibrate the model. The Þrst set of moments corresponds to input shares in agricultural output.
The second set of moments is related to properties of the size distribution of farms.
The moments corresponding to input shares are:16
• Land share of output.
• Value of horses/output.
• Value of tractors/output.
• Labor share of output.
• Ratio of hired to total labor.
In all cases except land share, the model’s predictions are complicated functions of the para-
meters. The theoretical counterparts of these moments (see the Appendix) are integrals of factor
demand functions with respect to the endogenous distribution of farmer’s skills.
Since heterogeneity of farmers plays such an important role in our story, we required the model
to match as many moments of the distribution of the variable ‘acres per farm’ –our measure of
Þrm size– as we could Þnd. To ensure consistency over the 1910-1960 period we restricted
16
The analogues in the model are in the Appendix.
18ourselves to moments for which time series evidence is available in a consistent manner. The best
information that we could obtain partitions the data into four bins. It includes information on the
number of farms for establishments of 49 acres or less, 50-499 acres, 500-999 acres and 1,000 or
more acres. We decided to merge the Þrst two categories, since we suspect that forces other than
agricultural prices affect the number of very small farms (less than 49 acres). In addition to this
information, we were able to Þnd some moments of the continuous size distribution. SpeciÞcally,
we have information on average farm size conditional on being in a certain size category.
In order to match the average farm size in 1910, ā, we adjusted total land area (A in the
model). Thus, we used a ‘free’ parameter to match this statistic.17 Note, however, that total
land area in 1960 is not a free parameter. We used data on Land in Farms (from the Historical
Statistics) to estimate the supply of land in 1960 –using our units– as
A60 = A10 × measured change in land in farms.
We are then left with Þve moments:
• Average acres per farm, conditional on the farm being in the 500-999 acre category, ā5−10 .
• Average acres per farm, conditional on the farm being in the 1,000 or more category, ā10+ .
• Fraction of land in farms in the 500-999 acre category, s5−10 .
• Fraction of land in farms in the 1,000 or more category, s10+ .18
• The coefficient of variation of ‘acres per farm.’
The calibration proceeds as follows. We choose the parameters so that the model –evaluated
at the 1910 prices– matches the 10 moments we obtained from the data. Since computing
the model’s predictions requires a Þxed point in the endogenously chosen ‘marginal’ farmer, e∗ ,
calibration is computationally intensive, and we were unable to match the data exactly. Table 1
spells out the parameters used to calibrate the model.
17
Alternatively, we could have endogeneized N̄ , the total mass of potential farmers, to match land. In our
numerical exercise we set N̄ = 1.
18
Given these statistics the fraction of farms in each category (the 0-499 acres is our residual) can be readily
computed.
19Parameter Ah αc αzy αny αz αk αh ρ µ̂ σ β ϕ n̂ γ
Value 3.7 0.86 0.37 0.4 0.55 0.72 0.6 -0.6 4 1.72 0.96 223 2 .015
Table 1: Calibration
The Þrst two columns of Table 2 present the match between the model and U.S. data for our
chosen speciÞcation for the year 1910. The match is fairly good in terms of most of the moments.
The one exception is the share of horses to output. Relative to the U.S. economy our speciÞcation
underpredicts the horse output ratio. It is not clear to us what is the reason. It is possible that
in 1910 horses were used to produce services not directly related to farming (e.g. transportation),
and that our simple model is not well equipped to capture this.
1910 1960
Moment Model Data Model Data Source
Land - share of output 0.198 0.2 0.198 0.2 Grilliches (1964)
Horses/output ratio 0.174 0.25 0.0066 0.01 Hist.Stat.of U.S.
Tractors/output ratio 0.0030 0.0031 0.133 0.135 Hist.Stat.of U.S.
Labor - share of output 0.47 0.5 0.381 0.401 Lebergott (1964)
C.V. of acres/farm 1.05 1.1 0.99 1.1 Hist.Stat.of U.S.
Labor - Hired/Total 0.27 0.24 0.24 0.26 Hist.Stat.of U.S.
ā5−10 617 646 716 695 Hist.Stat.of U.S.
s5−10 0.1 0.1 0.14 0.12 Hist.Stat.of U.S.
ā10+ 3414 3340 3662 3964 Hist.Stat.of U.S.
s10+ 0.19 0.19 0.38 0.49 Hist.Stat.of U.S.
Table 2: Match Between Model and Data, 1910 & 1960
The values of the calibrated parameters seem reasonable and, when there is evidence available,
fall in the range of estimates from micro studies. Of particular importance for our purposes is the
elasticity of substitution between horse services and tractor services. This elasticity –given by
1/(1 + ρ)– is calibrated to be equal to 2.5.19 The model also does pretty well in matching the
19
Our preferred value is slightly higher than the value of 1.7 estimated by Kislev and Petersen (1982). However,
20size distribution of farms.20
5 Steady States Results
We use the model — driven by the exogenous price sequences– to predict the levels of a variety of
variables in 1960. We then conduct a number of counterfactual experiments to illustrate the role
played by each of our modeling assumptions.
5.1 Baseline Model
The predictions of the model for the level of input use in agriculture in 1960 are also presented
in the last two columns of Table 2. These predictions were obtained by ‘feeding’ the 1960 values of
the exogenous processes to our baseline model and computing the 1960 steady state equilibrium.
Overall, the model performs extremely well in matching most of the moments in 1960. It does a
remarkable job capturing the increase in the tractor-output ratio from close to 0 in 1910 to 0.13
in 1960. It also predicts the decline of the horse. The horse-output ratio predicted by the model
declines from 0.17 in 1910 to 0.0066 in 1960, slightly less than the observed value of 0.01. Most
importantly, the model does get at the ‘right’ share of tractors in aggregate output, and also shows
a reduction in the value of horses relative to output. In terms of labor input, the baseline model
is quite successful at predicting the substantial decrease in the share of labor in agriculture (from
0.50 to 0.40 in the data, and 0.47 to 0.38 in the model).
The model predicts that the fraction of land held by the largest farms (1,000+ acres) rises
from 19% in 1910 to 38% in 1960. This parallels the observed change from 19% to 49%. The
model slightly overpredicts the average size of medium-sized farms (716 acres vs. 695 acres), and
it slightly underpredicts the size of the largest farms (3,662 acres vs. 3,964 acres) in 1960. Even
they completely ignored horses and their estimate is likely to be some weighted average of the two elasticites of
substitution: labor and capital and labor and horses.
20
The model produces a continuous distribution of farms (by farm size). We put the distribution in three bins
(0-499, 500-999, and 1000+) to match the evidence on acreage. We use this distribution to compute the moments
that we report. To compute mean conditional average acreage per farm we use (both for the model and the data)
a richer continuous distribution.
21though average farm size tripled, both model and data imply that the coefficient of variation of
farm size is roughly constant.
As indicated before, we adjusted measured TFP growth so that the increase in total output
predicted by the model and the data coincide in 1960. The required increase in TFP was 1.9. By
way of comparison, the Historical Statistics reports that overall farm TFP grew by a factor of 2.3.
Thus, around 17.4% of the increase in farm TFP between 1910 and 1960 can be accounted for by
the diffusion of the tractor, and the steady increase in average quality.
5.2 Sensitivity Analysis
As mentioned before, we view three features of the model as major determinants of the results:
selection, changes in prices (both wages and horse prices), and changes in tractor quality. To
analyze the quantitative role that each of these factors play in generating the results, we recompute
the predictions of the model for the year 1960 under alternative scenarios.
5.2.1 Changing the Driving Processes: Constant TFP
Our Þrst set of results takes TFP as given and asks: How well would the model predict tractor
adoption in 1960 if the driving processes were held at their 1910 level? This is a simple way of
assessing the importance of the included features in generating a good match between model and
data.
The results of those counterfactual exercises for the 1960-1910 ratio of tractors and output
ratio are summarized in Table 3.21
Baseline Holding Constant: U.S. data
w1910 v(x1910 ) Skill Dist. ph1910
Tractors 272 632 139 143 275 280
Output 2.1 5.53 1.58 1.19 2.15 2.1
Table 3: Changing the Driving Processes. No TFP Adjustment. 1960-1910 Ratios.
21
In the Appendix, we present more detailed data on the predictions of the alternative models for a variety of
variables in addition to output.
22The Þrst column gives the prediction of the baseline model. Our preferred speciÞcation predicts
a level of adoption that is fairly close (97%) to that observed in the data (272/280). All the
counterfactuals, i.e. the versions of the model in which a speciÞc driving force is Þxed, do not
perform well. The column labeled w1910 reports the prediction of the model when farm wages are
(counterfactually) kept at their (relatively low) 1910 values. In this case, the model overpredicts
the growth in the number of tractors by over 125%. This is mostly driven by the spectacular
increase in agricultural output predicted by the model, which exceeds observed increases by 160%.
We view this result as evidence that modeling technology adoption ignoring the effects of changes
in other input prices can lead to fairly erroneous conclusions.
The second experiment, reported in the column labeled v(x1910 ), is designed to gauge the role
of quality changes in the performance of the model. To this end, we Þxed tractor quality at its
1910 level for all periods. In this case, the model predicts that only half as many tractors would
be adopted in 1960 relative to the data. A third experiment involved substituting the assumption
of equilibrium migration, i.e. the equilibrium condition that migration is driven by a comparison
between urban and rural net income, with the assumption that migration was random. Formally,
we assume that the distribution of skills in 1960, µ̃, is now exogenously given by
Nf,60 1910
µ̃(e) = µ (e).
Nf,10
This speciÞcation ‘scales down’ the mass of farmers so as to match the decline in the total
number of farms between 1910 and 1960, but it assumes that the distribution of skills is unchanged.
Ignoring selection results in an underprediction of tractor adoption of the order of 50%.
Finally, we use the model to study what role –if any– the dramatic change in horse prices
had on the predictions of the model. Somewhat surprisingly, holding horse prices at their 1910
levels the model still correctly predicts tractor adoption in 1960. As we will argue later, changes
in horse prices do not have a large impact on the model’s predictions and, hence, were not an
important determinant of the speed of diffusion. However, it turns out that the existence of a
‘horse technology’ is essential since it gives a differential role to changes in real wages.
Thus, a tentative conclusion one draws from this exercise is that all the features that we
included in the model, with the possible exception of horses, are quite important to produce a
23good match to the data. However, some caution needs to be exercised. Recall that in the baseline
model we chose TFP –given its endogeneity– so as to match output. Thus, a much stronger
‘test’ of our baseline speciÞcation is to compare its predictions with those of the alternative models
where, in each case, TFP is allowed to adjust as to match the growth in agricultural output. We
now turn to those results.
5.2.2 Changing the Driving Processes: Adjusted TFP
In this section we describe the predictions of each of the four ‘counterfactuals’ when TFP is
adjusted so that each model matches the observed growth in agricultural output between 1910
and 1960. Of course, given that, by construction, output levels are matched, each model has to
be evaluated in terms of its ability to reproduce other moments.
Constant Wages As before, we set rural and urban wages at their 1910 levels and compute
the predictions of the model for 1960.22 The results are presented in the column labeled ‘w1910 ’
in Table 4. This version of the model underpredicts both the increase in the number of tractors
(193 vs. 280) and the decrease in the number of horses (1/5.11 vs. 1/7.8). As a result, the
horse-tractor ratio decreases by a factor of about 1,000 between 1910 and 1960. In the data (and
the baseline model) this factor is slightly above 2100. Thus, as suspected, the increase in wages
over this period had a substantial impact in driving the substitution between tractors and horses
and, hence, inßuences the speed of diffusion of the tractor. Moreover, this version induces much
less migration (there is no reason to migrate since wages are the opportunity cost of farming) and,
consequently, severely underpredicts the increase in farm size (1.3 vs. 2.13). This, in turn, leads
the model to overpredict the coefficient of variation of ‘acres per farm’ by approximately a third
(1.43 vs. 1.1)
The Importance of Quality-Adjustment Tractor quality increased throughout the period.
To quantify the contribution of quality changes to the results, we recomputed the model –with
22
TFP had to be adjusted by a factor of 1.18 to match the increase in output.
24Ratio:1960 to 1910 Baseline w1910 v(x1910 ) Random ph1910 U.S. Data
Acres/farm 2.56 1.34 2.74 2.56 2.61 2.13
Stock of Tractors 272 193 184 272 275 280
Stock of Horses 1/7.90 1/5.11 1/4.41 1/7.90 1/8.9 1/7.8
Stock of Labor 1/2.92 1/1.21 1/2.95 1/2.92 1/2.78 1/2.5
Price of Land 0.76 0.74 0.75 0.76 0.77 0.8
Farm Output 2.1 2.1 2.1 2.1 2.1 2.1
Level:1960
C.V. acres/farm 0.98 1.43 0.93 0.82 0.97 1.1
Hired Lab./Total 0.24 0.21 0.23 0.32 0.23 0.26
Table 4: Changing the Driving Processes: Ajusted TFP
the usual TFP adjustment23 – assuming that quality remained constant at the 1910 level. A
priori it is not obvious in what direction this pushes the results. Increases in the efficiency of
new tractors reduces the number of tractors required to perform a given task. On the other hand,
higher quality tractors result in lower costs of operations, and this increases the demand for tractor
services.
The results of holding v(x) constant at its 1910 level are in column labeled ‘v(x1910 )’ in Table
4. The number of tractors adopted in the absence of quality improvements would have been lower
than in the baseline case by about 32%. Similarly the horse-tractor ratio is predicted to decrease
by a factor of about 810, which is small when compared to the predictions of the baseline and
the observed U.S. values (about 2100). In terms of size distribution, the lack of quality changes
increases the effective price of operating a tractor and this, in turn, reduces proÞts in the farm
sector. Lower proÞts induce more migration and a substantial overprediction of the increase in
farm size (3.46 vs. 2.13)
Selective vs. Random Migration It is possible to show (see the Appendix for a formal proof)
that if the production function is Cobb-Douglas in managerial skill and other factors (as is the
23
In this case the adjustment factor was 2.7.
25case in our model), any aggregate level of input use (and total output) generated by the baseline
model can be replicated by the random migration version, given an appropriate adjustment in
TFP. The results of this experiment for the 1960-1910 ratio of several variables and the levels of
a couple of variables in 1960 are summarized in the column labeled ‘Random’ in Table 4. Thus,
to ascertain the ability of the model to match the data we need to consider moments that depend
on the size distribution. Along these lines, the random migration model fails in two dimensions:
it underpredicts the coefficient of variation of ‘acres per farm’ by 25% (0.82 vs. 1.1), and it
overpredicts the ratio of hired to total labor. More importantly, it gives counterfactual predictions
for some moments of the distribution of farm size. We will discuss this in more detail in the
analysis of the transitional dynamics.
The Role of Horse Prices Recent research on the topic of adoption of tractors has emphasized
that adjustment of horse prices delayed the diffusion of tractors (see Olmstead and Rhode (2001)).
We can use our model to study how would the adoption decision have changed had horse prices
not adjusted. The results are in the column ‘ph1910 ’ in Table 4. It follows that horse prices did not
play a major role. The number of tractors in 1960 would have been very similar to that observed in
the data. Of course, the horse-tractor ratio would have been higher, but in every other dimension
the model would have performed well.
Should we conclude that explicitly modeling the fact that farmers had a choice between an
‘old’ and a ‘new’ technology is an unnecessary feature of the model? No. The reason is simple:
had we ignored horse, we would have had only a minor impact from the change in wages, and this
would have severely limited the model’s ability to match the data. Explicitly modeling the choice
of technology is important insofar as it provides a channel through which other, complementary,
changes in prices affect the demand for tractors.
5.2.3 Changing the SpeciÞcation
In this section we present the result of modifying the speciÞcation of the production function
from the one used in the baseline to a ‘full’ Cobb-Douglas functional form. We also explore the
effect of (almost) eliminating the rents that accrue to farm operators. In all cases, we Þnd that
26the changes substantially worsen the model’s ability to match the data.
Elasticity of Substitution Our speciÞcation of the technology is such that, at our preferred pa-
rameterization, the elasticity of substitution between tractors and labor is 2.5, while the elasticity
of substitution between horses and labor is one. These differences in the elasticity of substitution
result in variable shares and, more importantly, suggest that wage changes can have an asymmetric
effect on the demand of horses and tractors. SpeciÞcally, we expect an increase in wages to induce
substitution of tractors for horses.
In order to quantitatively assess the importance of this speciÞcation, we studied a version of
the model in which ρ is set equal to 0. In this case, the production function is Cobb-Douglas
in all its variables. As before, we adjusted TFP growth so that the model exactly matches the
observed growth in output. TFP was increased by a factor of 1.72. The results for the 1960-1910
ratios and levels in 1960 of some important variables are in the column labeled ‘ρ = 0’ in Table 5.
It follows that the Cobb-Douglas speciÞcation severely underpredicts the diffusion of the tractor.
The reason for this result is simple: The Cobb-Douglas functional form implies constant input
shares. In the absence of spectacular price decreases in the own price –and tractor prices showed
a large, but not spectacular decrease over this period – the model predicts modest increases in
the quantities demanded.
Changes in the Share of Managerial Skills The assumption that managerial skills receive
a non-zero fraction of total revenue plays a signiÞcant role in our model, as it has an impact on
migration decisions. We considered a speciÞcation that signiÞcantly reduces the share of proÞts
that accrue to skill. The results are in the column labeled ‘αc = 0.999’ in Table 5.
The model underpredicts the number of tractors by 13% and, more importantly, predicts a
huge increase in average farm size. While in the data, the average acreage per farm increases by a
factor of 2.13, this speciÞcation predicts an increase four times as large. Of course, this is a direct
consequence of the higher elasticity of migration with respect to wages induced by the small share
of proÞts received by farm operators.
27Ratio: 1960 to 1910 Baseline ρ=0 αc = 0.999 U.S. Data
Acres/Farm 2.56 3.44 9.22 2.13
Stock of Tractors 272 4.93 245 280
Stock of Horses 1/7.90 1/1.96 1/8.34 1/7.8
Stock of Labor 1/2.92 1/2.46 1/2.85 1/2.5
Price of Land 0.76 1.31 0.78 0.8
Output 2.1 2.1 2.1 2.1
Level: 1960
C.V. acres/farm 0.99 1.02 3.47 1.1
Hired Lab./Total 0.24 0.27 0.73 0.26
Table 5: Changing the Production Function
6 Transitional Dynamics: Was Diffusion Too Slow?
The results for 1960 indicate that the model does a reasonable job of matching some of the key
features of the data. However, they are silent about the model’s ability to account for the speed
at which the tractor was adopted.
Was diffusion too slow? To answer this question, the entire dynamic path from 1910 to
1960 needs to be computed. To do this, we took the observed path for prices (pk , ph , pc , w, wF ),
operating costs (ck , ch , ca ) and depreciation rates (δ k , δ h , δ a ), and used them as inputs to compute
the predictions of the model for the 1910-1960 period.24 At the same time, we adjusted the
time path of TFP so that the model matches the data in terms of the time path of agricultural
output, the analog of our steady state procedure. This helps to get the scale right along the entire
transition. This exercise is computationally very intensive as it requires solving for the Þxed point
in the sequence of TFPs from 1910 to 1960, in addition to calculating the equilibrium in the land
24
We use Þve-year moving averages for all these sequences. For the years 1910 and 1960, we use actual data
(remember that these dates are viewed as steady-states). For all other years, the Þve year average was constructed
as the average of the the year in question, the two years before and the two years. In a sense, using a Þve year
average substitutes for the lack of adjustment costs in the model.
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